Simultaneous Small Noise Limit for Singularly Perturbed Slow-Fast Coupled Diffusions

Athreya, Siva R and Borkar, Vivek S and Kumar, K Suresh and Sundaresan, Rajesh (2019) Simultaneous Small Noise Limit for Singularly Perturbed Slow-Fast Coupled Diffusions. In: APPLIED MATHEMATICS AND OPTIMIZATION .

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Abstract

We consider a simultaneous small noise limit for a singularly perturbed coupled diffusion described by where B-t, W-t are independent Brownian motions on R-d and R-m respectively, b : R-d xR(m) -> R-d, U : R-d xR(m) -> R and s : (0, infinity) -> (0, infinity). We impose regularity assumptions on b, U and let 0 < alpha < 1. When s(e) goes to zero slower than a prescribed rate as epsilon -> 0, we characterize all weak limit points of X-epsilon, as epsilon -> 0, as solutions to a differential equation driven by a measurable vector field. Under an additional assumption on the behaviour of U(x, center dot) at its global minima we characterize all limit points as Filippov solutions to the differential equation.

Item Type:	Journal Article
Publication:	APPLIED MATHEMATICS AND OPTIMIZATION
Publisher:	SPRINGER
Additional Information:	Copyright of this article belongs to SPRINGER
Keywords:	Averaging principle; Slow-fast motion; Caratheodory solution; Filippov solution; Small noise limit; Nonlinear filter; Spectral gap; Reversible diffusion
Department/Centre:	Division of Electrical Sciences > Electrical Communication Engineering Division of Interdisciplinary Sciences > Robert Bosch Centre for Cyber Physical Systems
Date Deposited:	13 Dec 2019 11:36
Last Modified:	13 Dec 2019 11:36
URI:	http://eprints.iisc.ac.in/id/eprint/64045

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